An unknown was prepared with the concentration of 0.000630 M. A Beer's Law plot was prepared using the absorbance values from standard solutions of ASA and a line drawn through all the points passed through the origin with a slope of 1550.2 M–1. The expected absorbance and %T values for the diluted aspirin solution prepared by the student is

i know that the absorbance is .977 but i don't know how to work out A=log (1/T)

A = log (1/T)
Punch in 0.977 on your calculator.
Now take the antilog of 0.977 to obtain 1/T. To do that, hit the 10x key. The calculator display should read 9.48418. That is 1/T. Then take the reciprocal of that to obtain 0.10544. Multiply that by 100 to obtain 10.544%T. I have used more digits than allowed so you can check your display reading with mine. I hope this helps. I did not check your A value of 0.977. But A = 0.977 is %T of 10.5%.

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